Question

State whether it is possible for the figure described to exist. Write yes or no.

Three non-collinear points all lie in each of the two planes.

Short answer

No, it is not possible that three non-collinear points all lie in each of two planes.

Step-by-step solution

Step 1. Write the postulate 7.

Postulate 7 states that through any three non-collinear points exactly one plane can pass.

Step 2. Draw the diagram of plane X passing through three non-collinear points A, B, and C.

The figure represents the plane$X$ passing through three non-collinear points $A$,$B$ and$C$ is:

Step 3. State whether it is possible that three non-collinear points all lie in each of two planes by considering the postulate 7 and above diagram.

From the diagram and postulate 7, it can be noticed that if three points are non-collinear then exactly one plane can pass through these points. Therefore, it is not possible that any three non-collinear points can simultaneously lie on the two different planes.

Therefore, it is not possible that three non-collinear points all lie in each of the two planes.